Publication
Pacific Journal of Mathematics
Paper

Path partitions and packs of acyclic digraphs

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Abstract

Let G be an acyclic directed graph with |V(G)| ≥ k. We prove that there exists a colouring {C1, C2, …, Cm} such that for every collection {P1, P2, …, Pk} of k vertex disjoint paths with |Uj=1k Pj| a maximum, each colour class Ci, meets min{|Cl|, k} of these paths. An analogous theorem, partially interchanging the roles of paths and colour classes, has been shown by Cameron [4] and Saks [17] and we indicate a third proof. © 1985 by Pacific Journal of Mathematics.

Date

01 Jan 1985

Publication

Pacific Journal of Mathematics

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